TESTING/EIG/ssyt21.f(3)

NAME
TESTING/EIG/ssyt21.f

SYNOPSIS

  Functions/Subroutines
subroutine ssyt21 (itype, uplo, n, kband, a, lda, d, e, u, ldu, v, ldv, tau, work, result)
SSYT21

Function/Subroutine Documentation

  subroutine ssyt21 (integer itype, character uplo, integer n, integer kband, real, dimension( lda, * ) a, integer lda, real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldv, * ) v, integer ldv, real, dimension( * ) tau, real, dimension( * ) work, real, dimension( 2 ) result)

SSYT21

Purpose:

    !>
    !> SSYT21 generally checks a decomposition of the form
    !>
    !>    A = U S U**T
    !>
    !> where **T means transpose, A is symmetric, U is orthogonal, and S is
    !> diagonal (if KBAND=0) or symmetric tridiagonal (if KBAND=1).
    !>
    !> If ITYPE=1, then U is represented as a dense matrix; otherwise U is
    !> expressed as a product of Householder transformations, whose vectors
    !> are stored in the array  and whose scaling constants are in .
    !> We shall use the letter  to refer to the product of Householder
    !> transformations (which should be equal to U).
    !>
    !> Specifically, if ITYPE=1, then:
    !>
    !>    RESULT(1) = | A - U S U**T | / ( |A| n ulp ) and
    !>    RESULT(2) = | I - U U**T | / ( n ulp )
    !>
    !> If ITYPE=2, then:
    !>
    !>    RESULT(1) = | A - V S V**T | / ( |A| n ulp )
    !>
    !> If ITYPE=3, then:
    !>
    !>    RESULT(1) = | I - V U**T | / ( n ulp )
    !>
    !> For ITYPE > 1, the transformation U is expressed as a product
    !> V = H(1)...H(n-2),  where H(j) = I  -  tau(j) v(j) v(j)**T and each
    !> vector v(j) has its first j elements 0 and the remaining n-j elements
    !> stored in V(j+1:n,j).
    !>

Parameters
    ITYPE

    !>          ITYPE is INTEGER
    !>          Specifies the type of tests to be performed.
    !>          1: U expressed as a dense orthogonal matrix:
    !>             RESULT(1) = | A - U S U**T | / ( |A| n ulp ) and
    !>             RESULT(2) = | I - U U**T | / ( n ulp )
    !>
    !>          2: U expressed as a product V of Housholder transformations:
    !>             RESULT(1) = | A - V S V**T | / ( |A| n ulp )
    !>
    !>          3: U expressed both as a dense orthogonal matrix and
    !>             as a product of Housholder transformations:
    !>             RESULT(1) = | I - V U**T | / ( n ulp )
    !>

    UPLO

    !>          UPLO is CHARACTER
    !>          If UPLO='U', the upper triangle of A and V will be used and
    !>          the (strictly) lower triangle will not be referenced.
    !>          If UPLO='L', the lower triangle of A and V will be used and
    !>          the (strictly) upper triangle will not be referenced.
    !>

    N

    !>          N is INTEGER
    !>          The size of the matrix.  If it is zero, SSYT21 does nothing.
    !>          It must be at least zero.
    !>

    KBAND

    !>          KBAND is INTEGER
    !>          The bandwidth of the matrix.  It may only be zero or one.
    !>          If zero, then S is diagonal, and E is not referenced.  If
    !>          one, then S is symmetric tri-diagonal.
    !>

    A

    !>          A is REAL array, dimension (LDA, N)
    !>          The original (unfactored) matrix.  It is assumed to be
    !>          symmetric, and only the upper (UPLO='U') or only the lower
    !>          (UPLO='L') will be referenced.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of A.  It must be at least 1
    !>          and at least N.
    !>

    D

    !>          D is REAL array, dimension (N)
    !>          The diagonal of the (symmetric tri-) diagonal matrix.
    !>

    E

    !>          E is REAL array, dimension (N-1)
    !>          The off-diagonal of the (symmetric tri-) diagonal matrix.
    !>          E(1) is the (1,2) and (2,1) element, E(2) is the (2,3) and
    !>          (3,2) element, etc.
    !>          Not referenced if KBAND=0.
    !>

    U

    !>          U is REAL array, dimension (LDU, N)
    !>          If ITYPE=1 or 3, this contains the orthogonal matrix in
    !>          the decomposition, expressed as a dense matrix.  If ITYPE=2,
    !>          then it is not referenced.
    !>

    LDU

    !>          LDU is INTEGER
    !>          The leading dimension of U.  LDU must be at least N and
    !>          at least 1.
    !>

    V

    !>          V is REAL array, dimension (LDV, N)
    !>          If ITYPE=2 or 3, the columns of this array contain the
    !>          Householder vectors used to describe the orthogonal matrix
    !>          in the decomposition.  If UPLO='L', then the vectors are in
    !>          the lower triangle, if UPLO='U', then in the upper
    !>          triangle.
    !>          *NOTE* If ITYPE=2 or 3, V is modified and restored.  The
    !>          subdiagonal (if UPLO='L') or the superdiagonal (if UPLO='U')
    !>          is set to one, and later reset to its original value, during
    !>          the course of the calculation.
    !>          If ITYPE=1, then it is neither referenced nor modified.
    !>

    LDV

    !>          LDV is INTEGER
    !>          The leading dimension of V.  LDV must be at least N and
    !>          at least 1.
    !>

    TAU

    !>          TAU is REAL array, dimension (N)
    !>          If ITYPE >= 2, then TAU(j) is the scalar factor of
    !>          v(j) v(j)**T in the Householder transformation H(j) of
    !>          the product  U = H(1)...H(n-2)
    !>          If ITYPE < 2, then TAU is not referenced.
    !>

    WORK

    !>          WORK is REAL array, dimension (2*N**2)
    !>

    RESULT

    !>          RESULT is REAL array, dimension (2)
    !>          The values computed by the two tests described above.  The
    !>          values are currently limited to 1/ulp, to avoid overflow.
    !>          RESULT(1) is always modified.  RESULT(2) is modified only
    !>          if ITYPE=1.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 205 of file ssyt21.f.

Author

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